University, the word says it all: universal, so it's a jack of all trades. But let the universities, as we know them today, be just specialist factories.
Utimately, I agree with you. A balance between both is the right way to go. We don't want to know one thing only, because then we will be helpless when something outside of our area of expertise happens, or needs our attention. I had to choose one, so perhaps knowing a bit of everything is better than just being good at one thing.